Weighted Liapunov functions for a class of third-order autonomous differential equations

Abstract

1. Introduction. In 1963, Walter Leighton published a paper [7] in which he provided Liapunov functions for general classes of second-and third-order differential equations. In a subsequent paper [3], the current author and Walter Leighton considered Liapunov functions for second-order systems that were more general than those given in Leighton's 1963 paper. Further, this latter paper gave a class of weighted Liapunov functions for certain second-order systems. Further work utilizing weighted Liapunov functions for second-order equations was published by the current author in [1] and by S. Duchich and the current author in [2], A separate paper by A. Skidmore [8] extended Leighton's 1963 work on third-order equations to fourth-order equations, but no "weighting" was considered in either paper.The purpose of this paper is to extend Leighton's work (in [7]) on third-order systems by providing a class of weighted Liapunov functions for an equation